Magnesium m#etal has ΔHfusion = 9.037 kJ>mol and ΔSfusion = 9.79 J>1K mol2. What is the melting point of magnesium in °C? (LO 11.4) (a) 0.923 °C (b) 923 °C (c) 650 °C (d) 1.08 * 103 °C

Verified step by step guidance

1. Identify the given values: ΔH_fusion = 9.037 kJ/mol and ΔS_fusion = 9.79 J/(K mol).
2. Convert ΔH_fusion from kJ/mol to J/mol for consistency in units. Recall that 1 kJ = 1000 J.
3. Use the formula for the melting point (T_m) based on thermodynamics: T_m = ΔH_fusion / ΔS_fusion.
4. Plug the converted ΔH_fusion and ΔS_fusion values into the formula to calculate T_m in Kelvin.
5. Convert the temperature from Kelvin to Celsius using the formula: °C = K - 273.15.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and phase changes. It combines enthalpy (ΔH) and entropy (ΔS) into a single value, allowing us to determine if a process is spontaneous at constant temperature and pressure. The relationship is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Phase Change and Melting Point

The melting point of a substance is the temperature at which it transitions from solid to liquid. This process involves a change in enthalpy (ΔHfusion) and entropy (ΔSfusion). At the melting point, the Gibbs Free Energy change (ΔG) is zero, indicating that the solid and liquid phases are in equilibrium.

Calculating Melting Point

To find the melting point of magnesium, we can rearrange the Gibbs Free Energy equation to solve for temperature: T = ΔHfusion / ΔSfusion. By substituting the given values of ΔHfusion and ΔSfusion into this equation, we can calculate the melting point in Kelvin and then convert it to Celsius by subtracting 273.15.